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Paper detail

Lagrangian schemes for Wasserstein gradient flows

This paper reviews different numerical methods for specific examples of Wasserstein gradient flows: we focus on nonlinear Fokker-Planck equations,but also discuss discretizations of the parabolic-elliptic Keller-Segel model and of the fourth order thin film equation. The methods under review are of Lagrangian nature, that is, the numerical approximations trace the characteristics of the underlying transport equation rather than solving the evolution equation for the mass density directly. The two main approaches are based on integrating the equation for the Lagrangian maps on the one hand, and on solution of coupled ODEs for individual mass particles on the other hand.

preprint2020arXivOpen access
Jose A. CarrilloDaniel MatthesMarie-Therese Wolfram
math.NANumerical Analysis
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Jose A. CarrilloDaniel MatthesMarie-Therese Wolfram

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